Solve my Calculus 2 question. Here is a photo

Autumn Marie

Answered question

2022-06-06

karton

Expert2023-05-19Added 613 answers

To find two sets of parametric equations for the given rectangular equation

y = x^{5} + 5

, we can express

x

and

y

in terms of a parameter, usually denoted as

t

.
Set 1:
Let's choose

t

to represent

x

. Then the parametric equations are:

x = t

y = (t^{5} + 5)

Set 2:
Now, let's choose

t

to represent

y

. We can rearrange the equation

y = x^{5} + 5

to solve for

x

x = \sqrt[5]{y - 5}

y = t

In both sets of parametric equations,

t

serves as the parameter that allows us to vary

x

and

y

. By plugging in different values of

t

, we can generate corresponding pairs of

x

and

y

that satisfy the original equation

y = x^{5} + 5

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